Diffeomorphisms invariance
of the action (up to boundary terms) is proved
straightforwardly by using the Cartan identity \({\cal L}_{X}=i_Xd+di_X\)  for any
infinitesimal diffeomorfism generated by a vector field \(X\)  and recalling that the
action is the integral of a 4-form. Under these diffeomorphisms the
vector fields \(X_I\)  transform covariantly: \(\delta _XX_I=[X,X_I]\) . It is also possible to introduce \(\star \) -infinitesimal diffeomorphisms [1]}, see
discussion in [2]}, Section 8.2.4. They satisfy a deformed
Leibniz rule and leave invariant the vector fields \(X_I\)  and
hence the \(\star \) -product.
